Variational integrators are a class of structure-preserving integrators, that are derived by discretizing the action principle rather than the governing differential equation. The basic idea behind these methods is to obtain an approximation of the action integral called the discrete action. Stationary points of the discrete action give discrete time trajectories of the mechanical system. These integrators have good long-time energy behavior and they conserve the invariants of the dynamics in the presence of symmetries. The basics of variational integrators can be reviewed in [1]}, [2]} and more detailed theory can be found in [3]}. A more general framework encompassing variational integrators, asynchronous variational integrators, and symplectic-energy-momentum integrators is discussed in [4]}. Due to their symplectic nature, variational integrators are ideal for long-time simulation of conservative or weakly dissipative systems found in astrophysics and molecular dynamics. The discrete trajectories obtained using variational integrators display excellent energy behavior for exponentially long times.
